Question

↓↓↓ MATHS QUESTION ↓↓↓

☞ A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

× No Spam ×

Step-by-Step explanation required ✓✓

~~Topic:- Heron's Formula.​

Answer 1

$\huge{\underline{\underline{\mathfrak{Answer}}}}$

Figure is in the attachment

_____________________________

Given:

AB || CD

AB =25 m

CD= 10m

BC=14m

AD= 13m

From point C draw CE || DA . Hence ADCE is a ||grm having CD || AE & AD||CE

AE= CD= 10m

CE= AD= 13m

BE= AB- AE =25- 10=15 m

BE= 15m

In ∆BCE

BC= 14m, CE= 13m, BE= 15m

Semiperimeter (s)= (a+b+c)/2

Semiperimeter(s) =( 14+13+15)/2

s= 42/2= 21m

s= 21m

Area of ∆BCE= √ s(s-a)(s-b)(s-c)

Area of ∆BCE=√ 21(21-14)(21-13)(21-15)

Area of ∆BCE= √ 21×7× 8×6

Area of ∆BCE= √ 7×3× 7× 4×2×2×3

Area of ∆BCE=√7×7×3×3×2×2×4

Area of ∆BCE= 7×3×2×2= 21× 4= 84m²

Area of ∆BCE= 84m²

Area of ∆BCE= 1/2 × base × altitude

Area of ∆BCE= 1/2 × BE ×CL

84= 1/2×15×CL

84×2= 15CL

168= 15CL

CL= 168/15

CL= 56 /5m

Height of trapezium= 56/ 5m

Area of trapezium= 1/2( sum of || sides)( height)

Area of trapezium=1/2(25+10)(56/5)

Area of trapezium= 1/2(35)(56/5)

Area of trapezium= 7×28= 196m²

_____________________________

Hence the area of field is 196m²

Answer 2

$\huge\mathfrak\purple{Bonjour!!}$

$\huge\mathcal{Solution:-}$

♨ ANSWER:-

196 m²

♨ STEP-BY-STEP EXPLAINATION:-

→ Given:-

ABCD is a trapezium shaped field with parallel sides AB and DC measuring 25 m and 10 m respectively. The non-parallel sides AD and BC measures 14 m and 13 m respectively.

→To find:-

The area of the field.

→Construction:-

Draw DE || BC. Also draw DF perpendicular to AB.

→ Solution:-

DE=BC= 13 m. [Opposite sides of a parallelogram are equal]

and

AE= AB-EB

i.e.,

AE= AB-DC [Since EB || DC and EB=DC]

=> AE= (25-10)m

=>AE= 15m.

Now,

For ∆AED,

a= 14 m, b= 15 m, c=13m.

Therefore,

s= a + b + c/2 = 14 + 15 + 13/2 = 42/2 = 21 m.

Therefore,

Area of ∆AED = √s (s-a)(s-b)(s-c)

= √21(21-14)(21-15)(21-13)

=√21(7)(6)(8)

=√7×3×7×3×2×2×2×2

= 84 m².

Now, we need to find the height of the given triangle AED. For that, we need to equate the area with the formula, 1/2 × b× h. Here we go!

1/2 × AE × DF = 84 m²

=> 1/2 × 15 m × DF = 84 m²

=> DF = 84 × 2/15

=>DF = 56/5 = Height (h).

Now,

Area of the parallelogram EBCD = b × h.

= EB × DF

= 10 × 56/2

= 112 m²

Now,

The total area of the given field = Area of the ∆AED + Area of the parallelogram EBCD.

= 84 m² + 112 m²

= 196 m².

[Do have a glimpse at the attachment above to view the figure].

✔✔✔✔✔✔✔

Hope it helps...❣❣❣

⭐❤✨♥⭐❤✨♥⭐

Be Brainly...✌✌✌

♣ SRIPURNA ♠